Convergence to the Plancherel measure of Hecke eigenvalues
Volume 214 / 2024
Acta Arithmetica 214 (2024), 191-213
MSC: Primary 11F11; Secondary 11F25
DOI: 10.4064/aa230419-4-10
Published online: 12 February 2024
Abstract
We give improved uniform estimates for the rate of convergence to Plancherel measure of Hecke eigenvalues of holomorphic forms of weight $2$ and level $N$. These are applied to determine the sharp cutoff for the non-backtracking random walk on arithmetic Ramanujan graphs and to Serre’s problem of bounding the multiplicities of modular forms whose coefficients lie in number fields of degree $d$.
